We report the first observation on the 'Lehmann rotation' of the director configuration of flat cholesteric drops subjected to a DC electric field. This allows us to determine both the sign and the magnitude of the electromechanical coupling coeffi- cient VE of the chiral liquid crystal, which is approx 2x10-5 q in cgs units, where q is the wavevector of the helix, whose sign is positive (negative) for a right (left) handed cholesteric.